This paper addresses the problem of controlling quarter-vehicle semi-active suspension systems. Presently, the suspension system involves a magnetorheological (MR) damper featuring hysteretic behavior captured through the Bouc–Wen model. The control objective is to regulate well the chassis vertical position despite the road irregularities. The difficulty of the control problem lies in the nonlinearity of the system model, the uncertainty of some parameters and the inaccessibility to measurements of the hysteresis internal state variable. The control design is performed using Lyapunov control design tools; it includes an observer providing online estimates of the hysteresis internal state and an adaptive state-feedback regulator. The adaptive controller, obtained by combining the state observer and the state-feedback regulator, is formally shown to meet the desired control objectives. This theoretical result is confirmed by several simulations. The latter illustrate the performances of the present adaptive controller and compare them with those of earlier control approaches and those of the passive suspension.

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